Porcupine intervals

This is one possible naming and organization system for intervals of porcupine temperament. It's based on the porcupine[7] scale, or equivalently on the val <7 11 16|.

In 22edo, all the neighboring intervals on this chart that are shown as about 20 cents apart are actually the same. For example, the augmented third (9/7) and the diminished fourth (14/11) are both the same interval (8\22) in 22edo. This corresponds to 99/98 being tempered out in 22edo.

In 15edo, on the other hand, the intervals that are shown as about 40 cents apart are actually the same. For example, the augmented third (9/7), is now the same as a minor fourth (4/3) rather than a diminished one. That is because 28/27 is tempered out in 15edo.

Name	Size*	Ratio	No. of Porcupine Generators(~162.7¢)	Comments
Unisons
Perfect unison (P1)	0	1/1	0
Augmented unison (A1)	61.1	81/80~36/35~33/32~25/24	-7	And other ratios, of course
Seconds
Diminished second (d2)	101.6	21/20~16/15	8
Minor second (m2)	162.7	12/11~11/10~10/9~35/32	1
Major second (M2)	223.8	9/8~8/7	-6
Augmented second (A2)	284.9	Close to 13/11	-13	Also "subminor third"
Thirds
Diminished third (d3)	264.3	7/6	9	Also "supermajor second"
Minor third (m3)	325.4	6/5~11/9	2	Coincidentally familiar
Major third (M3)	386.5	5/4	-5	Coincidentally familiar
Augmented third (A3)	447.6	9/7 (close to 13/10)	-12	Also "subminor fourth"
Fourths
Diminished fourth (d4)	427.0	14/11	10	Also "supermajor third"
Minor fourth (m4)	488.1	4/3	3	Rather than "perfect fourth"
Major fourth (M4)	549.2	11/8	-4
Augmented fourth (A4)	610.3	10/7	-11	Also "subminor fifth"
Fifths
Diminished fifth (d5)	589.7	7/5	11	Also "supermajor fourth"
Minor fifth (m5)	650.8	16/11	4
Major fifth (M5)	711.9	3/2	-3	Rather than "perfect fifth"
Augmented fifth (A5)	773.0	11/7	-10	Also "subminor sixth"
Sixths
Diminished sixth (d6)	752.4	14/9 (close to 20/13)	12	Also "supermajor fifth"
Minor sixth (m6)	813.5	8/5	5	Coincidentally familiar
Major sixth (M6)	874.6	5/3	-2	Coincidentally familiar
Augmented sixth (A6)	935.7	12/7	-9	Also "subminor seventh"
Sevenths
Diminished seventh (d7)	915.1	Close to 22/13	13	Also "supermajor sixth"
Minor seventh (m7)	976.2	7/4~16/9	6
Major seventh (M7)	1037.3	9/5~11/6	-3
Augmented seventh (A7)	1098.4	15/8	-8
Octaves
Diminished octave (d8)	1138.9	21/11~35/18~160/81	7
Perfect octave (P8)	1200	2/1	0
Augmented octave (A8)	1261.1	81/40~45/22~33/16~25/12	-7

* In POTE 11-limit porcupine




See also: Porcupine Notation